Aris-Taylor dispersion in the subarachnoid space

A complete theory able to assess the longitudinal dispersion of a passive solute injected in an annular cavity subject to a pulsatile flow and a porous medium is provided. Aris-Taylor method of statistical moments is combined with the Brinkman approach for porous flows and morphological dispersion, in order to get an analytical relationship for the time-dependent enhanced dispersion coefficient. The application of intratechal drug delivery in the cerebrospinal fluid contained in the subaracnoid space is discussed in detail. The main result of the theory and its assumptions are also numerically validated through the use of a finite volume solver. The role of several physiological features, such as geometry, temporal frequency and wavelength of the pressure forcing are analyzed. It turns out that the presence of delicate strands of connective tissue, called trabeculae, that fill the cavity and link the innermost layer of meninges play a crucial role. They in fact induce extra terms of morphological dispersion and act sinergistically with pulsation to produce realistic times of drug delivery in clinically significant conditions. The results have potentials for the optimization of delivery protocols of drug therapies of the central nervous system.